"RuntimeWarning: overflow encountered in exp", but not when using an array-CodePudding

I am implementing the following formula:

in Python (with SciPy and NumPy). I wrote the following expression:

def fokker_plank_solution_1_sur(t, k, c, x_0):
    if k == 0 & c == 0:
        pass
    
    else:
        print("Case 2")
        t_1 = (k - c)/(k - 2*c)
        t_2 = np.exp((k * x_0   k*(k - 2*c)*t))
        t_3 = erfc((x_0   2 * (k - c) * t)/(np.sqrt(4*t)))
        t_4 = 0.5
        t_5 = erfc((- x_0   2 * c * t)/np.sqrt(4 * t))
        t_6 = k/(k - (2 * c))
        t_7 = np.exp(2 * c * x_0)
        t_8 = erfc((x_0   2*c*t)/(np.sqrt(4*t)))
        
        y = t_1 * t_2 * t_3   t_4 * (t_5 - t_6 * t_7 * t_8)
        
        return y

Case 1: If I am using the following conditions, I am getting "good" numbers (t_2 = 1.94e 05) and the plot

D = .25
x_val = np.linspace(1,500,250)
c = 0
x_0 = 5

for k in [.8]:
    y_val = fokker_plank_solution_1_sur(x_val * D, k, c, x_0)
                                                   |      |

    # print(np.concatenate((x_val.reshape([250,1]), y_val.reshape([250,1])), axis = 1))
    
    plt.plot(x_val, y_val)

Case 2: However, if I am just putting this in the console,

fokker_plank_solution_1_sur(np.array((50.0)) * .25, 10, 0, 0.8)
                                                     |       |

I get the return

t_2 = np.exp((k * x_0   k*(k - 2*c)*t))

RuntimeWarning: overflow encountered in exp

After some search, I found t_2 is just getting too big, to be further processed (1,2), t_2 is then

e^1258.0

-> So the question now is, why can python calculate numbers, when using a NumPy array indirectly (case 1), but not when using the NumPy array directly (case 2)? Thank you for reading this far.

CodePudding user response：

It depends on how you tell NumPy to handle errors. You can control it with seterr or errstate.

For example:

>>> with np.errstate(all='ignore'):
...    print(fokker_plank_solution_1_sur(np.array((50.0)) * .25, 10, 0, 0.8))
nan


>>> with np.errstate(all='warn'):
...     print(fokker_plank_solution_1_sur(np.array((50.0)) * .25, 10, 0, 0.8))

RuntimeWarning: overflow encountered in exp
  t_2 = np.exp((k * x_0   k * (k - 2 * c) * t))
RuntimeWarning: invalid value encountered in double_scalars
  y = t_1 * t_2 * t_3   t_4 * (t_5 - t_6 * t_7 * t_8)
nan


>>> with np.errstate(all='raise'):
...     print(fokker_plank_solution_1_sur(np.array((50.0)) * .25, 10, 0, 0.8))
Error
Traceback (most recent call last):
  [...]
  t_2 = np.exp((k * x_0   k * (k - 2 * c) * t))
FloatingPointError: overflow encountered in exp

You are likely using a different setting in your program and when you call the function from the console.